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Central Limit Theorem for $\mathbb{Z}_{+}^d$-actions by toral endomorphisms


 
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1. Title Title of document Central Limit Theorem for $\mathbb{Z}_{+}^d$-actions by toral endomorphisms
 
2. Creator Author's name, affiliation, country Mordechay Levin; Israel
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Central limit theorem, partially hyperbolic actions, toral endomorphisms
 
3. Subject Subject classification 60F15, 37A
 
4. Description Abstract In this paper we prove the central limit theorem  for the following multisequence
$$
\sum_{n_1=1}^{N_1} ... \sum_{n_d=1}^{N_d}   f(A_1^{n_1}...A_d^{n_d} {\bf x} )
$$
where $f$ is a Hölder's continue function, $A_1,\ldots,A_d$ are $s\times s$ partially hyperbolic commuting  integer matrices, and $\bf x$ is a uniformly distributed random variable in $[0,1]^s$. Next we prove the  functional central limit theorem, and the almost sure central limit theorem. The main tool is the $S$-unit theorem.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-03-11
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1904
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-1904
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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